Impacts of Surface Adsorption on Water Uptake within a Metal Organic Nanotube Material

The confinement-dependent properties of solvents, particularly water, within nanoporous spaces impart unique physical and chemical behavior compared to those of the bulk. This has previously been demonstrated for a U(VI)-based metal organic nanotube that displays ice-like arrays of water molecules within the 1-D pore space and complete selectivity to H2O over all other solvents and isotopologues. Based upon our previous work on D2O and HTO adsorption processes, we suggested that the water uptake was controlled by a two-step process: (1) surface adsorption via hydrogen bonding to hydrophilic amine and carboxylic groups and (2) diffusion of the water into the hydrophobic 1-D nanochannels. The current study seeks to evaluate this hypothesis and expand our existing kinetic model for the water diffusion step to account for the initial surface adsorption process. Vapor sorption experiments, paired with thermogravimetric and Fourier-transform infrared analyses, yielded uptake data that were fit using a Langmuir model for the surface-adsorption step of the mechanism. The water adsorption curve was designated a type IV Brunauer–Emmett–Teller isotherm, which indicated that our original hypothesis was correct. Additional work with binary solvent systems enabled us to evaluate the uptake in a range of conditions and determine that the uptake is not controlled by the vapor pressure but is instead completely dependent on the relative humidity of the system.

. Representative FTIR spectrum of the evolved gas produced from the TGA of the assynthesized UMONT material.

II.
Representative characterization of UMONT material after uptake of binary systems Figure S4. Representative TGA curve for ETOH 80 system where mass gain was measured at 1.8%. Figure S5. Representative FTIR for the evolved gas from the TGA of the ETOH 80 system indicating that water is the only solvent present in the UMONT material. Figure S6. Representative TGA curve for ACE50 system where mass gain was measured at 1.8%. Figure S7. Representative FTIR for the evolved gas from the TGA of the ACE50 system indicating that water is the only solvent present in the UMONT material. Figure S8. Representative TGA curve for HOAc20 system where mass gain was measured at 1.59%. Figure S9. Representative FTIR for the evolved gas from the TGA of the HOAc20 system indicating that water is the only solvent present in the UMONT material. Figure S10. Calculated PXRD of pure UMONT material (a) and PXRD post-exposure to acetic acid in HOAc20 in a batch set-up (b). Alignment of peaks indicates that the UMON is not degraded by acetic acid.

Characteristics for Langmuirian Adsorption
Langmuirian adsorption characterizes adsorption of species from a bulk phase to a surface. The principle assumptions for Langmurian adsorption are[Allen J. Bard  There are no interactions between the adsorbate species on the surface.
The surface is uniform and featureless.
The coverage of adsorbates is set by: the concentration of species in the bulk phase the energies of the species in the bulk phase and the adsorbate on the surface (characterized by an equilibrium constant) the number of surface sites available for adsorption.
At high concentration (activity) of the species in the bulk phase, the maximum surface coverage of the adsorbates is monolayer coverage.

Rate Expressions for Langmurian Adsorptions
The available (open) sites at time t is: For the bulk phase a gas, species X i in present in the bulk gas phase at concentration [X i ] g . The rate of adsorption and desorption of X i is characterized by rate constants. Species X i adsorbs to the surface with rate constant k f;i and desorbs with rate constant k b;i . The rate of adsorption of species i is For all surface coverages in units of mol cm 2 and [X i ] g the vapor pressure in torr (760 torr = 760 mm Hg = 1.00 atm = 101325 Pa), the units for k f;i and k b;i are torr 1 s 1 and s 1 .

Simple Langmuirian Model for Surface Adsorption -One Adsorbate
For a single adsorbate, equation 3 is:

Rate of adsorption for one species
Allow that the initial coverage is i (t = 0) = 0. Then, solved by Laplace transforms, i (t) the time dependent surface concentration of species i is found. The equilibrium constant, The time dependent conditions for the problem are satis…ed by (1) and (2). At time t 1=2 at half maximum coverage,

Equilibrium
From the rate expression at a given [X i ] g , equilibrium is achieved as t ! 1 and d i (t) =dt = 0. From equation 8 as t ! 1, the equilibrium and maximum surface coverage of i, The limiting, …nal, and maximum weight of adsorbate is i;max .

Rate Expression
Rearranging the rate expression equation 8, time dependent rate data are evaluated as A plot of ln ;i and intercept of zero.

The Experiment
The experiment measures total surface coverage P i=1 i (t) as weight adsorbed. To account for di¤erent initial sample weights, the weight fraction adsorbed is reported as w (t), the ratio of weight adsorbed with time normalized by the initial sample weight. The …nal equilibrium weight fraction is w max .
For a single adsorbate where weight fraction adsorbed is followed with time w (t), time dependent response is then reported.
Time is in seconds.
The vapor phase concentrations are expressed as vapor pressure. Here torr (mm Hg) are used. Vapor pressure of component i in a mixture of gas phase components is the product of the mole fraction of i in the gas phase x i and the saturation vapor pressure of component i at the experimental temperature and pressure, V i;sat , so that [X i ] g = x i V i;sat . For water in air at a speci…ed relative humidity %RH, the vapor pressure of water is tabulated. See for example http://www.respirometry.org/calculator/water-vapor-calculators.

Data Analysis
Data care analyzed as steady state and transient response.

Steady State Data Analysis
Where w (t) is tracked with time, w max is found as the …nal weight fraction. If only the …nal weight fraction is known, then w max is also known.
From this steady state analysis and equation 12, K [X] g for the single adsorbate at vapor pressure [X] g is found.
Given the vapor pressure of the adsorbate [X] g , K is found, where K = k f =k b . The equilibrium constant for adsorption K yields the free energy for adsorption G.

Transient Data Analysis
Where the weight fraction adsorbed w (t) is tracked as a function of time, k f and k b are determined. Equilibrium provides the values for max , K [X] g , and K, where Then, [X] g and w max are known and k f is determined.
Given K and k f , A plot of ln 1 vs t has intercept of zero and slope of wmax where w max is known. Note that as w (t) approaches w max , the argument of the ln will approach 0 and is unde…ned.

Model Equation Development
Consider For adsorption of species X in the gas phase at concentration [X] g at rate k f and desorption of adsorbed species at rate k b , the rate of change for the surface coverage of adsorbate is speci…ed.
Allow that the initial coverage is (t = 0) = 0. (We can make a greater than 0 value if needed. 0 (t) ) Into Laplace space, Substituting (t = 0) = 0 and rearranging, By partial fractions At nodes from equation 40, test of speci…cation: where the second expression is the Langmuirian isotherm.

IV. Data fitting for H2O and binary systems
Data were collected as weight adsorbed with time. Weights are normalized by the initial sample weight, w(t). A final weight adsorbed is expressed as a fraction wmax or percent wmax%. For most samples, more than one replicate was collected, specified as number in sample n. Where n > 1, the data were averaged and the average data were fit. Shown are the fits for each of the water (RH) and mixtures of water and another solvent. The quality of the fit varies with the system. In each of the following plots, the rightmost axis is represented by the orange data points and the grey points represent the model. The blue points lie on the leftmost axis.